The present invention generally relates to two-dimensional position detecting methods and apparatuses, and more particularly to a two-dimensional position detecting method and apparatus suited for detecting a two-dimensional position when positioning a semiconductor wafer, a mask and the like.
Recently, due to the high integration density of semiconductor integrated circuits, there is a demand to increase the fineness of patterns. As a result, the semiconductor wafer and the mask must be positioned with a high accuracy, and it is necessary to detect two-dimensional positions of the semiconductor wafer and the mask with a high accuracy.
FIG. 1A is a diagram for explaining a conventional one-dimensional position detecting method. A coherent light CL scans a diffraction grating 10 in a direction Y, where the diffraction grating 10 comprises gratings which extend in a direction X. A diffracted light DL which is generated with a predetermined angle to the coherent light CL is detected by a photosensor 11. FIG. 1B shows an output signal of the photosensor 11 relative to the scan position of the coherent light CL along the direction Y. The position of the diffraction grating 10 in the direction Y can be detected with a high accuracy from a peak position y.sub.0 where the output signal of the photosensor 11 becomes a maximum.
A description will now be given of the operating principle of a transmission type diffraction grating. As shown in FIG. 2A, a transmission type diffraction grating comprises openings 12 which are arranged periodically. The effects the opening 12 has on the amplitude and phase of the light are different from those of a periphery of the opening 12. The diffraction grating is located at a hatched portion on an XY-plane of an XYZ coordinate system shown in FIG. 2B. In FIG. 2A, l and s respectively denote the vertical and horizontal lengths of the opening 12, and d denotes the period of the openings 12 (or gratings). .xi.-axis and .eta.-axis respectively coincide with the X-axis and the Y-axis. It is assumed that the light originates from a point Q(x.sub.0, y.sub.0, z.sub.0) and the light received via the diffraction grating is monitored at a point P(x, y, z). R.sub.0 denotes a distance between an origin O and the point Q, and R denotes a distance between the origin O and the point P.
When there are N openings 12, a center (.xi..sub.n, .eta..sub.n) of each opening 12 can be obtained from the following set of formulas (1), where n=0, 1, . . . , N-1. ##EQU1## When the diffraction in the Fraunhofer region is considered by assuming that the distances R.sub.0 and R are sufficiently large compared to the size of the grating which is irradiated with the light, a light wave U at the point P can be obtained from the following formula (2), where k=2.pi./.lambda., .lambda. denotes the wavelength of light, p=.alpha.-.alpha..sub.0, q=.beta.-.beta..sub.0, .alpha..sub.0 =-x.sub.0 /R.sub.0, .alpha.=x/R, .beta..sub.0 =-y.sub.0 /R.sub.0, .beta.=y/R, and C denotes a constant. ##EQU2##
The light waves U(p, q) and U.sub.0 (p, q) can thus be described as follows by using the formulas (1) and (2). ##EQU3## Accordingly, the following formula (3) can be obtained. ##EQU4##
In addition, a light intensity J(p, q) can be described by the following formula (4), where J.sub.0 =.vertline.C.vertline..sup.2 s.sup.2 l.sup.2. ##EQU5##
From the formula (4), it is found that the diffracted light is generated in the direction kpd/2=m.pi. (m=0, .+-.1, .+-.2, . . . ), that is, in the direction .alpha.-.alpha..sub.0 =m.lambda./d. The light which corresponds to each m is referred to as an mth order spectrum.
FIG. 3 generally shows an essential part of an example of a conventional one-dimensional position detecting apparatus. A laser light emitted from a laser tube 20 is reflected by a mirror 21 and is irradiated on a reflection type diffraction grating 22 which extends in the direction X. A -1st order spectrum generated by the diffraction grating 22 is reflected by the mirror 21 and is received by a photosensor 23 which is provided in a vicinity of the laser tube 20. An angle .theta..sub.m which is formed between a mirror surface 21a of the mirror 21 and the Z-axis is set so that a zero order spectrum does not reach the photosensor 23 as a noise. In FIG. 3, the diffraction grating 21 is scanned in the direction Y which is perpendicular to the paper so as to detect the position along the direction Y.
The conventional one-dimensional position detecting apparatus simply detects the one-dimensional position of an object. Hence, a pair of such one-dimensional position detecting apparatuses must be used in order to detect a two-dimensional position of the object. But in this case, there is a problem in that the accuracy of the position detection becomes poor due to an error in the relative arrangement of the two one-dimensional position detecting apparatuses. In addition, there are problems in that the diffraction grating which is detected by one one-dimensional position detecting apparatus must be separated by a certain distance from the diffraction grating which is detected by the other one-dimensional position detecting apparatus, and each one-dimensional position detecting apparatus alone cannot determine a two-dimensional position of one point.